Symmetry breaking is one of the core concepts of condensed matter physics. To understand a system, the most important question to ask is: what is its underlying symmetry? Symmetry captures the fundamental physics needed to describe a system. Nevertheless, this philosophy does not always lead to complete understanding of a process. In some occasions, an even meaningful question to ask is: what are the properties that are independent of symmetry? The physics that are not affected by the geometrical properties are the key topics that will be discussed in this course (termed here as topology). Unlike symmetry arguments that deal with degeneration problems, those seemingly rare occasions that immune to geometrical changes will lead to fascinating consequences in condensed matters, from which one finds intrinsic implications of a quantum system.
The concept of topology has revolutionised condensed matter physics over the past decade, and keep spreading into a variety of research areas. Having a specialised course that introduces this magnificent philosophy becomes demanding for the purpose of training outstanding physicists. Moreover, the establishment of Topological Physics Laboratory in ShanghaiTech provides excellent opportunities for our students to percept this physics branch. <<Topology in Condensed Matters>> forms one of the unique lecture courses in ShanghaiTech, which aligns with the scope that our physics education embraces cutting-edge scientific researches.
This course is designed for undergraduate/graduate experimentalists who prepare to explore in-depth physics in condensed mater systems. I will focus on understanding a number of real systems from a topological perspective: how topological properties lead to novel physics, how to find those rare occasions, and how to measure them. I wish the students appreciate the elegancy of this mathematical concept, and will be able to apply it into their own studies. |